Gary:
When using ArchiCAD 9, you can go to File > Save As... and then set the Format to 8.1 Project to save the ArchiCAD 9 file in the ArchiCAD 8.1 format. This will drop from the file any features that are only available in ArchiCAD 9. You would need to do this every time you are moving the project from ArchiCAD 9 back to 8.1. It might make more sense to install ArchiCAD 8.1 on your home computer and only use ArchiCAD 8.1 for this project, rather than taking the chance that some of your work in ArchiCAD 9 gets modified or lost in ArchiCAD 8.1.
HTH
David